In belted radial tires for high performance cars such as sport cars, a steel belt composed of two plies of steel cords arranged in parallel with each other at an angle of 15 to 30 degrees with respect to the tire equator are hitherto widely employed. Such a steel belt, however, greatly increases the tire weight and lowers the fuel consumption performance, when constructed to endure against high speed running, for example over 200 km/h. In order to reduce a tire weight by using light material cords in the belt, the present inventor experimentally made and tested tires, wherein the belt is formed by spirally winding a high modulus aromatic polyamide fiber cord on the carcass. As a result, the inventor found that when such a high modulus single material cord is used in a spiral belt structure, the tread rigidity is excessively increased and steering stability and ride comfort are lost. Further, during a tire vulcanizing process through which the inside of the tire is pressurized by an inflated tube, the belt elongation becomes insufficient to press the tire against the mold, and as a result, sometimes the molding becomes incomplete, and undesirable stress and/or strain reside in the belt, tread rubber and so on.